The first step is to find the least common denominator. In this case, it is .

Then, you convert each fraction by multiplying the first fraction by  and the second fraction by .

Once you have both fractions with a common denominator, you can add the numerators.

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The least common denomiator (or least common multiple...same concept) is the least expression that both denominators can go into. I like to work step by step with each term. Let's start with the numerical coefficients.

The least common multiple of 12 and 60 is 60. You can figure this out by writing out multiples of 12 and 60 and seeing the first one they have in common.

Now let's move on to the a's.

There's an and an Therefore, their LCM is .

Do the same with the b's and the c's; and , respectively.

Now put those all together to get .

Since fractions cannot be subtracted, we will need to find the least common denominator.  In order to find the least common denominator, we will need to multiply the  and .

There is no number below this value where the factors of nine and sixteen will intersect.

The question only asked for the least common denominator, so we do not need to evaluate this.

The least common denominator is .

When there are two terms involved in a denominator, I like to look at each separately and combine at the end. For 2 and 7, the least common denominator is what thier product is, which is 14. Then, for and , is the LCD for that pair since it's the least common multiple of the two. Now, put your answers together to get: .

The least common denominator is found by finding what the least common multiple is.

The multiples of  are 

The multiples of  are 

The multiples of  are 

The lowest number that occurs in the three numbers listed is , which means you could add or subtract the fractions by converting them all to fractions with a denominator of .

To solve this equation, we must find the least common denominator to add the fractions.

Keep in mind that the denominator of the second term is the difference of squares, which can be rewritten as

This is the least common denominator.

Now, we multiply both sides of the equationby the LCD on top and bottom (this is essentially 1):

After canceling terms, we get

Now, we solve for x:

Let's first get all the known terms on one side of the equation:

We need to find a common denominator for all the fractions.  One easy way to do this is to multiply each fraction by the denominator on the other two:

We can now add the numerators together:

And simplify:

The least common denominator would be all of the denominators multiplied together:

To find the Least Common Denominator, we multiply the denominator of both terms together:

In order to solve for the least common denominator, multiply both denominators together.

This will require the FOIL method.

Simplify the right side.

The answer is: